Discrete Induction and Interval Partition as Dual Causal Enumeration

We present a self-contained analysis demonstrating the internal consistency between dis-crete induction and continuous interval partitioning. By introducing a reversible digit-mirroringenumeration, we show that convergent geometric series over the unit interval correspond tobackward causal resolution rather than forward construction. Divergence is shown to occur inthe indexing domain, not in the resolved quantity. This establishes a duality between countingand partitioning without invoking completed infinities or external set-theoretic axioms.